The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1
 0  2  0  0  2  2 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2a+2  2 2a^2+2a+2  0 2a 2a^2+2a  0 2a+2  2 2a  2 2a^2 2a^2+2a+2 2a 2a^2+2 2a  2 2a
 0  0  2  0 2a^2+2 2a^2+2a+2 2a 2a^2+2 2a^2+2 2a 2a^2+2 2a^2 2a 2a^2+2a+2 2a 2a  2  0  0 2a^2+2a+2 2a^2  2  2  2 2a^2 2a^2+2 2a+2 2a^2+2a+2
 0  0  0  2  2 2a^2+2a 2a^2+2a  2 2a^2+2 2a^2+2a 2a^2+2 2a^2+2 2a+2  2  2  0 2a^2+2a 2a^2+2 2a^2+2a 2a+2 2a 2a^2+2a+2 2a+2 2a^2+2a+2  2 2a+2 2a^2+2a+2 2a^2+2a

generates a code of length 28 over GR(64,4) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+616x^176+707x^184+3584x^189+798x^192+25088x^197+686x^200+658x^208+511x^216+119x^224

The gray image is a code over GF(8) with n=224, k=5 and d=176.
This code was found by Heurico 1.16 in 7.15 seconds.